Question

The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000507 mm. Assume a random sample of 53 sheets of metal resulted in an x⎯⎯ = .3333 mm. Calculate the 90 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.) The 90% confidence interval is from to

Answer 1

Answer: (0.3332, 0.33341)

Explanation:

Formula to find the confidence interval for population mean
`(\mu)` :

`\overline{x}\pm z^*(\sigma)/(√(n))`

, where n= Sample size

`\overline{x}` = sample mean.

`z^*` = Critical z-value (two-tailed)

`\sigma` = population standard deviation.

As per given , we have

n= 53

`\sigma=0.000507\ mm`

`\overline{x}=0.3333\ mm`

The critical values for 90% confidence interval :
`z^*=\pm1.645`

Now , the 90 percent confidence interval for the true mean metal thickness:

`0.3333\pm (1.645)(0.000507)/(√(53))\\\\=0.3333\pm(1.645)(0.0000696)\approx0.3333\pm0.00011456\\\\=(0.3333-0.00011456,\ 0.3333+0.00011456)\\\\=(0.33318544,\ 0.33341456)\approx(0.3332,\ 0.3334)`

Hence, the 90 percent confidence interval for the true mean metal thickness. : (0.3332, 0.3334)